Reconstruction Method Based On Multi-residual And Non-negative Constraints Sparse

In recent years, the problem of recovering sparse signal from compressed measurements and solving underdetermined systems making use of sparsity characteristics have drawn considerable attentions among researchers in signal processing as well as mathematical communities. The typical applications include medical image and astronomical observation. On the other hand, to sparsely represent a signal upon an overcompleted basis also arises in signal processing problems. The above two classes of problems are sparse approximation of signal and sparse signal recovery respectively. Recently, a new theory called Compressive Sampling/Compressed Sensing (CS) received tremendous intrests. In Radar applications, the targets scene can be regarded as sparse in range-Doppler space, therefore CS theory shows great potential in improving Radar resolution.As one of the various sub-optimal methods for solving the problem mentioned above, the Greedy methods have been widely studied and utilized. This thesis proposes two generalized greedy algorithms in order to improve the performance of sparse signal recovery. The works presented in this thesis focus on the following aspects:(1) As the application background of the algorithms concerned in this thesis, the two classes of problem are introduced and defined, which are the problem of sparse approximation of signal and the problem of sparse signal recovery. The newly emerged area of Compressed Sampling is also briefly introduced.(2) The classical greedy methods are analyzed in detail, including whose core ideas and shortcomings. The direction for improvement is also discussed.(3) By generalizing the traditional concept of single residual, a new multi-residual is defined, and based on which a greedy algorithm is proposed. The performance of the new algorithm for recovering sparse signal is shown by computer simulations.(4) In dealing with the problem of non-negative sparse signal recovery, a concept of maximizing coefficients is introduced and based on which a new type of greedy algorism are proposed. Computer simulations illustrate the performance of the new methods.